A hot water tap can fill a bath in 5 minutes while a cold water tap can fill the same bath in 3 minutes. The drain pipe can empty the full bath in $\frac{4}{15}$.

A hot water tap can fill a bath in 5 minutes while a cold water tap can fill the same bath in 3 minutes. The drain pipe can empty the full bath in $\frac{4}{15}$. The two taps and the drain pipe are fully open for 1$\frac{1}{2}$ minutes after which the drain pipe is closed. How long will it take to fill the bath?

Answers

Fraction retained per minute

when all pipes are opened


= $\frac{1}{5} + \frac{1}{3} - \frac{4}{15}$

= $\frac{3 + 5 - 4}{15}$ = $\frac{4}{15}$

Fraction retained for

1$\frac{1}{2}$ minutes = $\frac{4}{15} \times \frac{3}{2}$

= $\frac{2}{5}$

Fraction to be filled

= 1 - $\frac{2}{5} = \frac{3}{5}$

Fraction added by hot and cold water tap

= $\frac{1}{5} + \frac{1}{3} = \frac{8}{15}$

Therefore to fill the bath it will take

$\frac{15}{8} \times \frac{3}{5} = \frac{9}{8}$ = 1$\frac{1}{8}$ minutes

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johnmulu answered the question on March 6, 2017 at 08:09

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